Q: Monochromatic light falls on two narrow slits that are $$0.05\ \mathrm{mm}$$ apart. On a screen $$4.00\ \mathrm{m}$$ away, the first order fringe (bright spot) is $$6.00\ \mathrm{cm}$$ from the center. What is the wavelength of the light?

$$5.0 \times 10$$^{-7}$$\ \mathrm{m}$$

Q: For the above engine cycle, which process corresponds to the heat $$Q_H$$ absorbed from the high temperature reservoir?

The isobaric expansion $$A \to B$$

Question 1

Monochromatic light falls on two narrow slits that are $$0.05\ \mathrm{mm}$$ apart. On a screen $$4.00\ \mathrm{m}$$ away, the first order fringe (bright spot) is $$6.00\ \mathrm{cm}$$ from the center. What is the wavelength of the light?

Accepted Answer

$$5.0 	imes 10$$^{-7}$$\ \mathrm{m}$$

Question 2

Monochromatic light of wavelength $$500\ \mathrm{nm}$$ falls on two narrow slits $$0.04\ \mathrm{mm}$$ apart, generating an interference pattern on a distant screen. At what angle (in degrees) does the first minima occur?

Accepted Answer

$$1.07^\circ$$

Question 3

A light beam traveling through air ($$n=1.00) $$reflects perpendicularly off the top and bottom surfaces of a thin layer of oil ($$n=1.50) $$floating on water ($$n=1.33). $$What is the thinnest layer of oil that will give rise to constructive interference at a wavelength of $$700\ \mathrm{nm}$$?

Accepted Answer

$$175\ \mathrm{nm}$$

Question 4

A soap film ($$n=1.35) of $$thickness $$150\ \mathrm{nm} is $$surrounded by air ($$n=1.00) on $$both sides. If light of a certain wavelength is beamed at the soap film perpendicular to its surface, what is the longest wavelength of light for which you’ll see no reflection?

Accepted Answer

$$600\ \mathrm{nm}$$

Question 5

The displacement of a transverse wave on a string is given by $$D(x,t) = 4 \sin(5\pi x - 6\pi t). $$What is the speed of the traveling wave?

Accepted Answer

$$1.2\ \mathrm{m/s}$$

Question 6

For the wave $$D(x,t) = 4 \sin(5\pi x - 6\pi t)$$, what is the period of the wave?

Accepted Answer

$$\dfrac{1}{6}\ \mathrm{s}$$

Question 7

For the same wave $$D(x,t) = 4 \sin(5\pi x - 6\pi t)$$, what is the wavelength?

Accepted Answer

$$0.5\ \mathrm{m}$$

Question 8

A standing sound wave is shown in a $$30\ \mathrm{cm}$$ long open tube. Which of the following wave functions best describes the displacement for the standing wave?

Accepted Answer

$$A \sin(kx) \cos(\omega t)$$

Question 9

What is the wavelength of the standing wave shown in a $$30\ \mathrm{cm}$$ long open tube, if the pattern shows the fundamental mode?

Accepted Answer

$$30\ \mathrm{cm}$$

Question 10

Assume the speed of sound in air is $$343\ \mathrm{m/s}. If $$your friend is at rest and playing an open pipe with a fundamental wavelength of $$0.30\ \mathrm{m}$$, and you run toward your friend at $$10\ \mathrm{m/s}$$, what frequency will you hear?

Accepted Answer

$$2944\ \mathrm{Hz}$$

Question 11

Two wind pipes are played together, one at $$1143\ \mathrm{Hz}$$ and the other at $$1146\ \mathrm{Hz}. $$What is the wavelength corresponding to the beat frequency?

Accepted Answer

$$343\ \mathrm{m}$$

Question 12

A monoatomic ideal gas undergoes a cycle: isobaric expansion from $$(P_1$, V_1$) to$$ $$(P_1$, 2V_1)$$, isochoric cooling to $$(P_2$, 2V_1)$$, and adiabatic compression back to $$(P_1$, V_1$). $$What is the ratio $$\dfrac{P_2$}{P_1$}$$ after the isochoric step?

Accepted Answer

$$0.63$$

Question 13

For the above engine cycle, what is the heat $$Q_{AB}$$ absorbed during the isobaric expansion from $$V_1 to$$ $$2V_1$$?

Accepted Answer

$$Q_{AB} = \dfrac{5}{2} P_1$ V_1$

Question 14

During the isochoric process $$B 	o C in $$the engine cycle, what is the heat $$Q_{BC}$$ exchanged?

Accepted Answer

$$Q_{BC} = \dfrac{3}{2} (P_2$ - P_1$) 2V_1$$

Question 15

For the above engine cycle, which process corresponds to the heat $$Q_H$$ absorbed from the high temperature reservoir?

Accepted Answer

The isobaric expansion $$A 	o B$$

Question 16

For the above engine cycle, what is the efficiency $$e of $$the cycle (to two significant digits)?

Accepted Answer

$$0.37$$

Question 17

For the isobaric expansion $$A 	o B in $$the engine cycle, what is the change in entropy $$\Delta S_{AB}$$?

Accepted Answer

$$nR \ln 2$$

Question 18

A student observes a soap film in white light and sees bright green ($$\lambda = 540\ \mathrm{nm}) $$reflected at normal incidence. If the index of refraction of the film is $$1.33$$, what is the minimum thickness of the film?

Accepted Answer

$$203\ \mathrm{nm}$$

PHY222 Midterm #2 – Step-by-Step Physics Guidance

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